Subgroups — C₅×#83937 #14439126

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5176	C₂	1	2	yes	maximal, complemented
8	C₅×#5175	C₂	1	2	yes	maximal, complemented
9	C₅×#5154	C₂	1	2	yes	maximal, complemented
10	C₅×#5151	C₂	1	2	yes	maximal, complemented
11	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3151	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	—	2	2	no	—
16	C₂×C₅×#235	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₅×#949	—	2	4	no	—
23	C₅×#947	C₂²	1	1	yes	characteristic, complemented
24	C₅×#944	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#215	C₂²	1	2	yes	complemented
26	C₅×#940	—	2	2	no	—
27	C₅×#940	C₂²	1	2	yes	—
28	C₅×#940	C₂²	1	2	yes	—
29	C₅×#940	C₂²	1	1	yes	characteristic, complemented
30	C₅×#939	—	2	2	no	—
31	C₅×#936	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#214	C₂²	1	2	yes	complemented
33	C₅×#932	—	2	4	no	—
34	C₂×C₅×#213	C₂²	1	2	yes	complemented
35	C₂×C₅×#213	C₂²	1	2	yes	complemented
36	C₄×C₅×#67	—	2	2	no	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₅×#208	C₂²	1	1	yes	characteristic
39	C₅×#908	—	2	4	no	—
40	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
41	C₂×C₅×#204	C₂²	1	2	yes	complemented
42	C₅×#815	C₂²	1	2	yes	complemented
43	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
44	#83937	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
46	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
47	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
48	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, complemented
49	C₅×#532	—	3	1	no	—
50	C₂×C₅×#127	—	3	1	no	—
51	C₅×#496	—	3	2	no	—
52	C₅×#496	—	3	2	no	—
53	C₅×#493	—	3	2	no	—
54	C₅×#492	—	3	2	no	—
55	C₄×C₅×M₁₆	—	3	1	no	—
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₂³×C₅×D₃	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×#67	—	2	1	no	—
70	C₂×C₅×#67	—	2	2	no	—
71	C₂×C₅×#67	—	2	4	no	—
72	C₂×C₅×#67	—	2	4	no	—
73	C₂×C₅×#67	—	4	8	no	—
74	C₂²×C₅×Dic₃	D₄	1	2	yes	—
75	C₅×#235	—	2	2	no	—
76	C₅×#235	—	2	2	no	—
77	C₂×C₅×D₁₂	—	2	2	no	—
78	C₂×C₅×D₁₂	—	2	2	no	—
79	C₂×C₅×D₁₂	—	2	1	no	—
80	C₂×C₅×D₁₂	C₂³	1	2	yes	—
81	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
82	C₂×C₄×C₅×D₃	—	2	1	no	—
83	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
84	C₃×C₅×SD₁₆	—	2	4	no	—
85	C₃×C₅×D₈	—	2	4	no	—
86	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
87	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
88	C₅×#217	—	2	2	no	—
89	C₅×#215	—	2	4	no	—
90	C₅×#214	—	2	4	no	—
91	C₅×#213	—	2	4	no	—
92	C₅×#213	—	2	4	no	—
93	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
94	C₅×Dic₃⋊C₄	—	2	2	no	—
95	C₄×C₅×Dic₃	D₄	1	2	yes	—
96	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₅×#208	D₄	1	4	yes	complemented
99	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
100	C₅×D₂₄	—	2	4	no	—
101	C₅×#204	—	2	4	no	—
102	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
103	#5832	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#949	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#932	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×#908	C₂×C₅	1	1	yes	characteristic, complemented
108	#5176	C₂×C₅	1	2	yes	complemented
109	#5175	C₂×C₅	1	2	yes	complemented
110	#5154	C₂×C₅	1	2	yes	complemented
111	#5151	C₂×C₅	1	2	yes	complemented
112	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₅×#41	—	3	1	no	—
114	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
115	C₂²×C₅×D₄	—	3	1	no	—
116	C₂²×C₅×D₄	—	6	2	no	—
117	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
118	C₅×AGL(1,ℤ/8)	—	2	4	no	—
119	C₅×AGL(1,ℤ/8)	—	6	4	no	—
120	C₅×AGL(1,ℤ/8)	—	6	4	no	—
121	C₅×AGL(1,ℤ/8)	—	6	4	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×SD₁₆	—	3	2	no	—
124	C₂×C₅×SD₁₆	—	3	2	no	—
125	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
126	C₂×C₅×D₈	—	3	2	no	—
127	C₂×C₅×D₈	—	3	2	no	—
128	C₂×C₅×D₈	—	3	2	no	—
129	C₂×C₅×D₈	C₂×D₃	1	2	yes	complemented
130	C₂×C₅×M₁₆	—	3	1	no	—
131	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
132	C₅×C₄⋊Q₈	—	3	1	no	—
133	C₅×#127	—	3	2	no	—
134	C₅×#127	—	3	2	no	—
135	C₅×#127	—	3	1	no	—
136	C₅×#127	—	6	2	no	—
137	C₅×#124	—	3	1	no	—
138	C₅×#124	—	3	1	no	—
139	C₅×#121	—	6	2	no	—
140	C₄×C₅×D₄	—	6	2	no	—
141	C₂×C₄²×C₅	—	3	1	no	—
142	C₅×#97	—	3	2	no	—
143	C₄×C₅×C₈	—	3	2	no	—
144	#3151	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	4	4	no	—
148	C₂³×C₃×C₅	—	4	2	no	—
149	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₅×D₃	—	2	1	no	—
151	C₂²×C₅×D₃	—	2	2	no	—
152	C₂²×C₅×D₃	—	4	4	no	—
153	C₂²×C₅×D₃	—	4	2	no	—
154	C₃×C₅×Q₈	—	2	1	no	—
155	C₃×C₅×Q₈	—	2	1	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	2	2	no	—
158	C₃×C₅×D₄	—	2	1	no	—
159	C₃×C₅×D₄	—	2	2	no	—
160	C₃×C₅×D₄	—	4	2	no	—
161	C₃×C₅×D₄	—	4	2	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	4	2	no	—
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₅×#67	—	4	8	no	—
169	C₅×#67	—	4	2	no	—
170	C₅×#67	—	4	4	no	—
171	C₅×#67	—	4	8	no	—
172	C₂×C₅×Dic₃	—	2	4	no	—
173	C₂×C₅×Dic₃	—	2	1	no	—
174	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
175	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
176	C₅×D₁₂	—	2	2	no	—
177	C₅×D₁₂	—	2	1	no	—
178	C₅×D₁₂	—	2	1	no	—
179	C₅×D₁₂	—	2	2	no	—
180	C₅×D₁₂	—	4	2	no	—
181	C₄×C₅×D₃	—	4	2	no	—
182	C₅×Dic₆	—	2	1	no	—
183	C₅×Dic₆	—	2	1	no	—
184	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
185	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
186	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂²×#67	—	2	2	no	—
189	C₂×#235	C₂²×C₅	1	1	yes	characteristic
190	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
191	C₃×AGL(1,ℤ/8)	—	2	4	no	—
192	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
193	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
194	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
195	#949	—	2	4	no	—
196	#947	C₂²×C₅	1	1	yes	characteristic, complemented
197	#944	C₂²×C₅	1	1	yes	characteristic, complemented
198	C₂×#215	C₂²×C₅	1	2	yes	complemented
199	#940	—	2	2	no	—
200	#940	C₂²×C₅	1	2	yes	—
201	#940	C₂²×C₅	1	2	yes	—
202	#940	C₂²×C₅	1	1	yes	characteristic, complemented
203	#939	—	2	2	no	—
204	#936	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₂×#214	C₂²×C₅	1	2	yes	complemented
206	#932	—	2	4	no	—
207	C₂×#213	C₂²×C₅	1	2	yes	complemented
208	C₂×#213	C₂²×C₅	1	2	yes	complemented
209	C₄×#67	—	2	2	no	—
210	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
211	C₂×#208	C₂²×C₅	1	1	yes	characteristic
212	#908	—	2	4	no	—
213	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
214	C₂×#204	C₂²×C₅	1	2	yes	complemented
215	#815	C₂²×C₅	1	2	yes	complemented
216	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
217	C₂⁴×C₅	—	2	1	no	—
218	C₂⁴×C₅	—	6	1	no	—
219	C₅×#41	—	2	2	no	—
220	C₅×#41	—	2	2	no	—
221	C₅×#41	—	6	2	no	—
222	C₅×#41	—	6	2	no	—
223	C₂×C₅×Q₈	—	3	1	no	—
224	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₅×D₄	—	2	1	no	—
226	C₂×C₅×D₄	—	2	2	no	—
227	C₂×C₅×D₄	—	2	1	no	—
228	C₂×C₅×D₄	—	2	2	no	—
229	C₂×C₅×D₄	—	3	1	no	—
230	C₂×C₅×D₄	—	3	2	no	—
231	C₂×C₅×D₄	—	6	2	no	—
232	C₂×C₅×D₄	—	6	4	no	—
233	C₂×C₅×D₄	—	6	4	no	—
234	C₂×C₅×D₄	—	6	1	no	—
235	C₂×C₅×D₄	—	6	2	no	—
236	C₂×C₅×D₄	—	6	1	no	—
237	C₂×C₅×D₄	—	6	2	no	—
238	C₂×C₅×D₄	—	12	8	no	—
239	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
240	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
241	C₂²×C₄×C₅	—	2	1	no	—
242	C₂²×C₄×C₅	—	3	2	no	—
243	C₂²×C₄×C₅	—	6	1	no	—
244	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₅×SD₁₆	—	2	4	no	—
246	C₅×SD₁₆	—	6	4	no	—
247	C₅×SD₁₆	—	6	4	no	—
248	C₅×SD₁₆	—	6	4	no	—
249	C₅×D₈	—	2	4	no	—
250	C₅×D₈	—	6	4	no	—
251	C₅×D₈	—	6	4	no	—
252	C₅×D₈	—	6	4	no	—
253	C₅×M₁₆	—	3	4	no	—
254	C₅×M₁₆	#67	1	4	yes	complemented
255	C₂×C₅×C₈	—	3	2	no	—
256	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
257	C₅×C₄⋊C₄	—	6	2	no	—
258	C₅×C₂²⋊C₄	—	6	2	no	—
259	C₅×C₂²⋊C₄	—	6	2	no	—
260	C₄²×C₅	—	3	2	no	—
261	C₄²×C₅	—	3	1	no	—
262	C₄²×C₅	—	3	1	no	—
263	C₂×AGL(1,ℤ/8)	—	3	1	no	—
264	C₂×AGL(1,ℤ/8)	—	3	1	no	—
265	C₂×AGL(1,ℤ/8)	—	3	1	no	—
266	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
267	#532	—	3	1	no	—
268	C₂×#127	—	3	1	no	—
269	#496	—	3	2	no	—
270	#496	—	3	2	no	—
271	#493	—	3	2	no	—
272	#492	—	3	2	no	—
273	C₄×M₁₆	—	3	1	no	—
274	C₂²×C₃×C₅	—	2	2	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	4	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	—	8	4	no	—
280	C₂²×C₃×C₅	#127	1	2	yes	—
281	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₅×D₃	—	4	1	no	—
283	C₂×C₅×D₃	—	4	2	no	—
284	C₂×C₅×D₃	—	4	4	no	—
285	C₂×C₅×D₃	—	4	2	no	—
286	C₂×C₅×D₃	—	8	4	no	—
287	C₃×C₄×C₅	—	4	1	no	—
288	C₃×C₄×C₅	#127	1	2	yes	—
289	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
290	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₅×Dic₃	—	2	2	no	—
292	C₅×Dic₃	—	4	1	no	—
293	C₅×Dic₃	AGL(1,ℤ/8)	1	4	yes	complemented
294	C₂⁴×C₃	—	2	1	no	—
295	C₂³×D₃	—	2	1	no	—
296	C₃×#41	—	2	2	no	—
297	C₃×#41	—	2	2	no	—
298	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
299	C₂×C₃×D₄	—	2	1	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	2	no	—
302	C₂×C₃×D₄	—	2	1	no	—
303	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂×#67	—	2	1	no	—
308	C₂×#67	—	2	2	no	—
309	C₂×#67	—	2	4	no	—
310	C₂×#67	—	2	4	no	—
311	C₂×#67	—	4	8	no	—
312	C₂²×Dic₃	C₅×D₄	1	2	yes	—
313	#235	—	2	2	no	—
314	#235	—	2	2	no	—
315	C₂×D₁₂	—	2	2	no	—
316	C₂×D₁₂	—	2	2	no	—
317	C₂×D₁₂	—	2	1	no	—
318	C₂×D₁₂	C₂³×C₅	1	2	yes	—
319	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
320	C₂×C₄×D₃	—	2	1	no	—
321	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
322	C₃×SD₁₆	—	2	4	no	—
323	C₃×D₈	—	2	4	no	—
324	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
325	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
326	#217	—	2	2	no	—
327	#215	—	2	4	no	—
328	#214	—	2	4	no	—
329	#213	—	2	4	no	—
330	#213	—	2	4	no	—
331	(C₂×D₃)⋊C₄	—	2	2	no	—
332	Dic₃⋊C₄	—	2	2	no	—
333	C₄×Dic₃	C₅×D₄	1	2	yes	—
334	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
335	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
336	#208	C₅×D₄	1	4	yes	complemented
337	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
338	D₂₄	—	2	4	no	—
339	#204	—	2	4	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	4	4	no	—
343	C₂³×C₅	—	4	2	no	—
344	C₂³×C₅	—	6	1	no	—
345	C₂³×C₅	—	6	2	no	—
346	C₂³×C₅	—	12	4	no	—
347	C₂³×C₅	—	12	2	no	—
348	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
349	C₅×Q₈	—	2	1	no	—
350	C₅×Q₈	—	2	1	no	—
351	C₅×Q₈	—	6	1	no	—
352	C₅×Q₈	—	6	1	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	2	no	—
355	C₅×D₄	—	2	1	no	—
356	C₅×D₄	—	2	2	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	2	no	—
359	C₅×D₄	—	6	1	no	—
360	C₅×D₄	—	6	2	no	—
361	C₅×D₄	—	6	1	no	—
362	C₅×D₄	—	6	2	no	—
363	C₅×D₄	—	12	4	no	—
364	C₅×D₄	—	12	8	no	—
365	C₅×D₄	—	12	8	no	—
366	C₅×D₄	—	12	2	no	—
367	C₅×D₄	—	12	2	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	3	2	no	—
370	C₂×C₄×C₅	—	3	2	no	—
371	C₂×C₄×C₅	—	4	2	no	—
372	C₂×C₄×C₅	—	6	4	no	—
373	C₂×C₄×C₅	—	6	1	no	—
374	C₂×C₄×C₅	—	12	2	no	—
375	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
376	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
377	C₂×C₄×C₅	C₂×#67	1	2	yes	—
378	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
379	C₅×C₈	—	3	4	no	—
380	C₅×C₈	C₂×#67	1	4	yes	complemented
381	C₂×#41	—	3	1	no	—
382	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
383	C₂²×D₄	—	3	1	no	—
384	C₂²×D₄	—	6	2	no	—
385	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
386	AGL(1,ℤ/8)	—	2	4	no	—
387	AGL(1,ℤ/8)	—	6	4	no	—
388	AGL(1,ℤ/8)	—	6	4	no	—
389	AGL(1,ℤ/8)	—	6	4	no	—
390	C₂×SD₁₆	—	3	2	no	—
391	C₂×SD₁₆	—	3	2	no	—
392	C₂×SD₁₆	—	3	2	no	—
393	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
394	C₂×D₈	—	3	2	no	—
395	C₂×D₈	—	3	2	no	—
396	C₂×D₈	—	3	2	no	—
397	C₂×D₈	C₂×C₅×D₃	1	2	yes	complemented
398	C₂×M₁₆	—	3	1	no	—
399	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
400	C₄⋊Q₈	—	3	1	no	—
401	#127	—	3	2	no	—
402	#127	—	3	2	no	—
403	#127	—	3	1	no	—
404	#127	—	6	2	no	—
405	#124	—	3	1	no	—
406	#124	—	3	1	no	—
407	#121	—	6	2	no	—
408	C₄×D₄	—	6	2	no	—
409	C₂×C₄²	—	3	1	no	—
410	#97	—	3	2	no	—
411	C₄×C₈	—	3	2	no	—
412	C₂×C₃×C₅	—	2	2	no	—
413	C₂×C₃×C₅	—	8	1	no	—
414	C₂×C₃×C₅	—	8	2	no	—
415	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
416	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₅×D₃	—	8	1	no	—
418	C₅×D₃	—	8	2	no	—
419	C₂³×C₃	—	2	1	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	4	4	no	—
422	C₂³×C₃	—	4	2	no	—
423	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂²×D₃	—	2	1	no	—
425	C₂²×D₃	—	2	2	no	—
426	C₂²×D₃	—	4	4	no	—
427	C₂²×D₃	—	4	2	no	—
428	C₃×Q₈	—	2	1	no	—
429	C₃×Q₈	—	2	1	no	—
430	C₃×D₄	—	2	1	no	—
431	C₃×D₄	—	2	2	no	—
432	C₃×D₄	—	2	1	no	—
433	C₃×D₄	—	2	2	no	—
434	C₃×D₄	—	4	2	no	—
435	C₃×D₄	—	4	2	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	4	2	no	—
438	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
440	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
441	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
442	#67	—	4	8	no	—
443	#67	—	4	2	no	—
444	#67	—	4	4	no	—
445	#67	—	4	8	no	—
446	C₂×Dic₃	—	2	4	no	—
447	C₂×Dic₃	—	2	1	no	—
448	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
449	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
450	D₁₂	—	2	2	no	—
451	D₁₂	—	2	1	no	—
452	D₁₂	—	2	1	no	—
453	D₁₂	—	2	2	no	—
454	D₁₂	—	4	2	no	—
455	C₄×D₃	—	4	2	no	—
456	Dic₆	—	2	1	no	—
457	Dic₆	—	2	1	no	—
458	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
459	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
460	C₂²×C₅	—	2	2	no	—
461	C₂²×C₅	—	4	4	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	1	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	8	4	no	—
466	C₂²×C₅	—	12	4	no	—
467	C₂²×C₅	—	12	2	no	—
468	C₂²×C₅	—	12	1	no	—
469	C₂²×C₅	—	12	2	no	—
470	C₂²×C₅	—	24	4	no	—
471	C₂²×C₅	#940	1	2	yes	—
472	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
473	C₄×C₅	—	3	4	no	—
474	C₄×C₅	—	4	1	no	—
475	C₄×C₅	—	6	2	no	—
476	C₄×C₅	—	12	1	no	—
477	C₄×C₅	#940	1	2	yes	—
478	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
479	C₄×C₅	C₂²×#67	1	1	yes	characteristic
480	C₂⁴	—	2	1	no	—
481	C₂⁴	—	6	1	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	6	2	no	—
485	#41	—	6	2	no	—
486	C₂×Q₈	—	3	1	no	—
487	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	3	1	no	—
493	C₂×D₄	—	3	2	no	—
494	C₂×D₄	—	6	2	no	—
495	C₂×D₄	—	6	4	no	—
496	C₂×D₄	—	6	4	no	—
497	C₂×D₄	—	6	1	no	—
498	C₂×D₄	—	6	2	no	—
499	C₂×D₄	—	6	1	no	—
500	C₂×D₄	—	6	2	no	—
501	C₂×D₄	—	12	8	no	—
502	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
503	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	3	2	no	—
506	C₂²×C₄	—	6	1	no	—
507	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
508	SD₁₆	—	2	4	no	—
509	SD₁₆	—	6	4	no	—
510	SD₁₆	—	6	4	no	—
511	SD₁₆	—	6	4	no	—
512	D₈	—	2	4	no	—
513	D₈	—	6	4	no	—
514	D₈	—	6	4	no	—
515	D₈	—	6	4	no	—
516	M₁₆	—	3	4	no	—
517	M₁₆	C₅×#67	1	4	yes	complemented
518	C₂×C₈	—	3	2	no	—
519	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
520	C₄⋊C₄	—	6	2	no	—
521	C₂²⋊C₄	—	6	2	no	—
522	C₂²⋊C₄	—	6	2	no	—
523	C₄²	—	3	2	no	—
524	C₄²	—	3	1	no	—
525	C₄²	—	3	1	no	—
526	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	4	1	no	—
529	C₂²×C₃	—	4	2	no	—
530	C₂²×C₃	—	4	4	no	—
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	8	4	no	—
533	C₂²×C₃	C₅×#127	1	2	yes	—
534	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
535	C₂×D₃	—	4	1	no	—
536	C₂×D₃	—	4	2	no	—
537	C₂×D₃	—	4	4	no	—
538	C₂×D₃	—	4	2	no	—
539	C₂×D₃	—	8	4	no	—
540	C₃×C₄	—	4	1	no	—
541	C₃×C₄	C₅×#127	1	2	yes	—
542	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
543	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
544	Dic₃	—	2	2	no	—
545	Dic₃	—	4	1	no	—
546	Dic₃	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
547	C₂×C₅	—	2	2	no	—
548	C₂×C₅	—	8	2	no	—
549	C₂×C₅	—	8	1	no	—
550	C₂×C₅	—	24	2	no	—
551	C₂×C₅	—	24	1	no	—
552	C₂×C₅	D₃×AGL(1,ℤ/8)	1	2	yes	—
553	C₂×C₅	C₂×#940	1	1	yes	characteristic
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	6	1	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	12	4	no	—
561	C₂³	—	12	2	no	—
562	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
563	Q₈	—	2	1	no	—
564	Q₈	—	2	1	no	—
565	Q₈	—	6	1	no	—
566	Q₈	—	6	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	6	1	no	—
574	D₄	—	6	2	no	—
575	D₄	—	6	1	no	—
576	D₄	—	6	2	no	—
577	D₄	—	12	8	no	—
578	D₄	—	12	4	no	—
579	D₄	—	12	8	no	—
580	D₄	—	12	2	no	—
581	D₄	—	12	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	3	2	no	—
584	C₂×C₄	—	3	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	6	4	no	—
587	C₂×C₄	—	6	1	no	—
588	C₂×C₄	—	12	2	no	—
589	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
590	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
591	C₂×C₄	C₂×C₅×#67	1	2	yes	—
592	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
593	C₈	—	3	4	no	—
594	C₈	C₂×C₅×#67	1	4	yes	complemented
595	C₂×C₃	—	2	2	no	—
596	C₂×C₃	—	8	2	no	—
597	C₂×C₃	—	8	1	no	—
598	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
599	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
600	D₃	—	8	2	no	—
601	D₃	—	8	1	no	—
602	C₅	#83937	1	1	yes	characteristic, direct product factor, Sylow
603	C₂²	—	2	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	8	4	no	—
609	C₂²	—	12	4	no	—
610	C₂²	—	12	2	no	—
611	C₂²	—	12	1	no	—
612	C₂²	—	12	2	no	—
613	C₂²	—	24	4	no	—
614	C₂²	C₅×#940	1	2	yes	—
615	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
616	C₄	—	3	4	no	—
617	C₄	—	4	1	no	—
618	C₄	—	6	2	no	—
619	C₄	—	12	1	no	—
620	C₄	C₅×#940	1	2	yes	—
621	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
622	C₄	C₂²×C₅×#67	1	1	yes	characteristic
623	C₃	C₅×#3151	1	1	yes	characteristic, complemented, Sylow
624	C₂	—	2	2	no	—
625	C₂	—	8	2	no	—
626	C₂	—	8	1	no	—
627	C₂	—	24	2	no	—
628	C₂	—	24	1	no	—
629	C₂	C₅×D₃×AGL(1,ℤ/8)	1	2	yes	—
630	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₅×#3151
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₂×C₅×#940	C₂	semidirect
5. C₂×C₅×#932	C₂	semidirect
6. C₂×C₅×#908	C₂	semidirect
7. C₅×#5176	C₂	semidirect
8. C₅×#5175	C₂	semidirect
9. C₅×#5154	C₂	semidirect
10. C₅×#5151	C₂	semidirect
11. C₅×Dic₃×M₁₆	C₂	semidirect
19. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
20. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₅×#947	C₂²	semidirect
24. C₅×#944	C₂²	semidirect
25. C₂×C₅×#215	C₂²	semidirect
29. C₅×#940	C₂²	semidirect
31. C₅×#936	C₂²	semidirect
32. C₂×C₅×#214	C₂²	semidirect
34. C₂×C₅×#213	C₂²	semidirect
35. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×D₂₄	C₂²	semidirect
41. C₂×C₅×#204	C₂²	semidirect
42. C₅×#815	C₂²	semidirect
43. C₅×C₈×Dic₃	C₂²	semidirect
44. #83937	C₅	direct (N × H)
48. C₂×C₅×AGL(1,ℤ/8)	D₃	semidirect
86. C₃×C₅×M₁₆	D₄	semidirect
98. C₅×#208	D₄	semidirect
102. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
103. #5832	C₂×C₅	semidirect
104. C₂×#949	C₂×C₅	semidirect
105. C₂×#940	C₂×C₅	semidirect
106. C₂×#932	C₂×C₅	semidirect
107. C₂×#908	C₂×C₅	semidirect
108. #5176	C₂×C₅	semidirect
109. #5175	C₂×C₅	semidirect
110. #5154	C₂×C₅	semidirect
111. #5151	C₂×C₅	semidirect
112. Dic₃×M₁₆	C₂×C₅	semidirect
125. C₂×C₅×SD₁₆	C₂×D₃	semidirect
129. C₂×C₅×D₈	C₂×D₃	semidirect
184. C₃×C₅×C₈	C₂×D₄	semidirect
185. C₅×C₃⋊C₈	C₂×D₄	semidirect
192. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
193. C₂×C₃×D₈	C₂²×C₅	semidirect
196. #947	C₂²×C₅	semidirect
197. #944	C₂²×C₅	semidirect
198. C₂×#215	C₂²×C₅	semidirect
202. #940	C₂²×C₅	semidirect
204. #936	C₂²×C₅	semidirect
205. C₂×#214	C₂²×C₅	semidirect
207. C₂×#213	C₂²×C₅	semidirect
208. C₂×#213	C₂²×C₅	semidirect
213. C₂×D₂₄	C₂²×C₅	semidirect
214. C₂×#204	C₂²×C₅	semidirect
215. #815	C₂²×C₅	semidirect
216. C₈×Dic₃	C₂²×C₅	semidirect
254. C₅×M₁₆	#67	semidirect
266. C₂×AGL(1,ℤ/8)	C₅×D₃	semidirect
293. C₅×Dic₃	AGL(1,ℤ/8)	semidirect
324. C₃×M₁₆	C₅×D₄	semidirect
336. #208	C₅×D₄	semidirect
380. C₅×C₈	C₂×#67	semidirect
393. C₂×SD₁₆	C₂×C₅×D₃	semidirect
397. C₂×D₈	C₂×C₅×D₃	semidirect
458. C₃×C₈	C₂×C₅×D₄	semidirect
459. C₃⋊C₈	C₂×C₅×D₄	semidirect
517. M₁₆	C₅×#67	semidirect
526. C₃×C₅	#3151	semidirect
546. Dic₃	C₅×AGL(1,ℤ/8)	semidirect
594. C₈	C₂×C₅×#67	semidirect
602. C₅	#83937	direct (N × H)
623. C₃	C₅×#3151	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₅×#5832	2
C₂×C₅×#949	2
C₂×C₅×#940	2
C₂×C₅×#932	2
C₂×C₅×#908	2
C₅×#5176	2
C₅×#5175	2
C₅×#5154	2
C₅×#5151	2
C₅×Dic₃×M₁₆	2
C₅×#3151	3
#83937	5

Subgroups — C5×#83937 #14439126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83937 #14439126